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Derivation

1. Initial program 0.3

   \[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]

2. Initial simplification0.3

   \[\leadsto \frac{1 - \tan x \cdot \tan x}{\tan x \cdot \tan x + 1}\]
3. Using strategy rm

4. Applied add-log-exp1.1

   \[\leadsto \frac{1 - \color{blue}{\log \left(e^{\tan x \cdot \tan x}\right)}}{\tan x \cdot \tan x + 1}\]
5. Using strategy rm

6. Applied exp-prod1.1

   \[\leadsto \frac{1 - \log \color{blue}{\left({\left(e^{\tan x}\right)}^{\left(\tan x\right)}\right)}}{\tan x \cdot \tan x + 1}\]

7. Applied log-pow0.3

   \[\leadsto \frac{1 - \color{blue}{\tan x \cdot \log \left(e^{\tan x}\right)}}{\tan x \cdot \tan x + 1}\]

8. Final simplification0.3

   \[\leadsto \frac{1 - \log \left(e^{\tan x}\right) \cdot \tan x}{1 + \tan x \cdot \tan x}\]

Runtime

Time bar (total: 11.6s)Debug logProfile

herbie shell --seed 2018339 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))